Pertanika J. Sci. & Techno!. 14(1 & 2): 33 - 40 (2006)ISSN: 0128-7680

© Universiti Putra Malaysia Press

Thermal Wave Resonant Cavity Technique in MeasuringThermal Diffusivity of Sucrose Solution

Azmi, B.Z., Sing, L.T., Saion, E.B. & Wahab, ZA.Department of Physics, Faculty of Science, Universiti Putra Malaysia,

43400 UPM Serdang, Selangor, Malaysia

Received: 11 December 2003

ABSTRAK

Teknik 'rongga resonan gelombang terma' telah digunakan untuk mengukurkeresapan terma bagi larutan sukrosa dengan kepersisan tinggi sehingga tigaangka bererti. Keresapan terma dari larutan adalah menu run denganpeningkatan peratusan berat sukrosa dan bersetuju dengan peraturan campuranmudah dalam renj sehingga ke suatu takat tepu. Juga keresapan terma larutanberubah secara linear terhadap kuasa dua FWHM. Nilai keresapan terma bagiair adalah amat hampir dengan nilai literatur.

ABSTRACT

The thermal-wave resonant cavity technique has been used to measure thermaldiffusivity of sucrose solution with precision up to three-significant-figure. Thethermal diffu ivity of the solution decreases linearly with the increase of sucroseweight percentage and agrees to the simple mixture rule in the range up to asaturated point. Also the solution thermal diffusivity varies linearly with squareFWHM. The thermal diffusivity value of water is very close to the literaturevalue.

Keywords: PVDF, photothermal

INTRODUCTION

Recent developments in monitoring and measuring the thermal properties ofliquids by using photothermal techniques have attracted much attention. Oneof the technique is thermal-wave resonant cavity (TWRC) and has been appliedsuccessfully to acetone in water to determine thermal effusivity (Balderas-Lopezet al. 2000), to various liquids to determine thermal diffusivity (Balderas-Lopezet al. 2001), specific heat capacity and thermal conductivity (Caerels et al. 1998),to air and gas to measure thermodynamic equation of state (Pan and Mandelis,1998), thermal diffusivity (Wang and Mandelis 1999), absolute infrared emissivity(Shen and Mandelis 1995; Shen et al. 1998) and monitor hydrocarbon vapours(Lima and Marin 2000).

The photothermal detector used in TWRC technique is a thin pyroelectric(PE) transducer such as polyvinylidene diflouride (PVDF) film that has strongPE effect (Kawai 1969; Bergman et al. 1971; Mandelis and Zver 1985; Xiao andLang 1989; Mandelis et al. 1993) to detect the modulated or pulsed temperaturerise induced in the material. The technique uses a modulated optical sourcethat is a common feature of all photothermal techniques to generate thermalwaves. The length and propagation characteristics of a thermal wave are simply

Azmi, B.Z., Sing, L.T., Saion, E.B. & Wahab, ZA.

controlled by the frequency of the light source modulator. The spatial behaviourof the thermal wave in 1WRC technique is monitored by varying the cavitylength at one modulation frequency.

In this paper the 1WRC technique application in monitoring the thermaldiffusivity of sucrose solution is described as the saturated sucrose solution isdiluted to low concentration at room temperature.

THEORY AND METHOD

The development of a photopyroelectric (PPE) detector with a various sample­to-source distance has successfully introduced the variability of the thermal­wave cavity length at single modulation frequency as another equally powerfulcontrol parameter. In order to analyse quantitatively PE quadrature data fromthe materials which are very weak sources of thermal waves, a general onedimensional treatment which takes into account all the energy pathways anddetermines explicitly the dependences of the PE signal on each and all systemparameters (Mandelis et at. 1993). The one-dimensional theoretical geometry isshown in Fig. 1. When intensity modulated of light is illuminated onto a metalfoil a thermal wave will be generated and then propagates to a medium nextto it. By placing a PE sensor physically in contact with the medium the PEvoltage will be detected. At a fixed thermal-wave oscillation frequency, f = OJ /

2n, the PE voltage signal across the detector is given by (Balderas-Lopez et at.2000; Shen and Mandelis 1995).

(1)

where OJ is the angular frequency of light chopper, L is the cavity length, and0", is the complex thermal diffusion coefficient, defined by

(2)

at is the thermal diffusivity of the liquid sample. The interfacial thermalcoefficients 'ljk are defined as

(3)

where bjk

= ej

/ ek is the thermal coupling coefficient, the ratio of thermaleffusivities of media j and k, the subscripts s, p, and t refer to the thermal-wavesource, the PE material and the liquid sample, respectively.

34 PertanikaJ. Sci. & Techno!' Va!. 14 os. 1 & 2, 2006

Thermal Wave Resonant Cavity Technique in Measuring Thermal Diffusivity of Sucrose Solution

The magnitude of the complex expression given in Eqn. (1) can be writtenas

(4)

(5)

where f is the light chopping frequency.The plot of the in-phase signal versus cavity length from Eqn. (4) is a curve

that has a deep valley of depth !Pmin followed by a small peak of height !pm.x"

From this, a 'full width at half maximum' (FWHM) is defined as the width ofthe curve in unit length at half maximum of the in-phase signal. The half

maximum signal here is the half maximum of the curve height or t(IPmax + IPmin ).

The TWRC cell was constructed by using a thin copper foil attached to oneend of a glass tube and the intensity modulated laser beam was illuminated onthe foil to induce thermal wave, Fig. 1. Since the foil is in direct contact withthe liquid sample, the thermal wave generated propagates across the liquid toreach the PVDF film PE sensor. The tube is attached to a micropositioner toalter the foil position thus altering the cavity length, L. The small PE voltagesignal was fed into a pre-amplifier for signal amplification and then into a lock­in amplifier for signal analysis. The cavity length was increased by 20-micronstep, and at each step the lock-in magnitude and phase signals were recorded.By plotting In (signal) versus cavity length L, the thermal diffusivity can beobtained from the plot gradient AI using Eqn. (5). Also by plotting in-phasesignal versus L the FWHM can be obtained for the particular liquid sample.

In the following this technique is used to test a 'simple mixture rule' onthermal diffusivity in liquid media mixture. For a mixture containing x w% ofmedium A of thermal diffusivity aA and (1 - x) w% of medium B of thermaldiffusivity then the mixture thermal diffusivity of the media a

Bcan be written

as

(6)

RESULTS AND DISCUSSION

A saturated sucrose solution at room temperature (about 23°C) was preparedby desolving 10.5 g sucrose in 10.0 ml distilled water, i.e. the sucrose weightpercentage in water is about 51.2w%. The other lower w%'s sucrose solutionwere made by adding proportionate weight of water in the saturated solution.In the experiment the light chopping frequency was set at 7.60Hz and care has

PertanikaJ. Sci. & Technol. Vol. 14 Nos. 1 & 2,2006 35

Azmi, B.Z., Sing, L.T., Saion, E.B. & Wahab, ZA.

J'q ·d --------1

,I

---

J'\ ])1

Fig. 1: Schematic diagram of thermak-wave resonant cavity cell

been taken to ensure no stray light off the glass tube hitting the PE sensor asthis will introduce unwanted noise produced by the sensor.

From 9 data sets of 8 sucrose solutions of various w%'s and one of distilledwater, the overal variation of PE voltage signal versus cavity length L is displayedin a 3-D spline surface plot in Fig. 2. The signal decreases exponentialy withcavity length for all w%'s but with different exponential constants. Here, theplain distilled water produces the highest PE signal of all sucrose solutions.

From Eqn.(4), the thermal diffusivity is obtained by plotting In (signal)versus cavity length and for a particular case of 6.4w% sucrose solution is as canbe seen in Fig. 3. The plot gradient is an exponential constant and the plot

Fig. 2: Plot of PE voltage versus cavity length at various sucrose w %

36 PertanikaJ. Sci. & Techno!. Va!. 14 as. 1 & 2, 2006

Thennal Wave Resonant Cavity Technique in Measuring Thennal Diffusivity of Sucrose Solution

is linear fitted by using Microsoft Origin software. The gradient and the thermaldiffusivity are 130.860cm-1 and 0.139 1O-2 cm2/s, respectively. Here, the gradientis obtained by fitting only the first 15 data points that contribute to the goodfit because at very large L they deviate from the line as the noise dominates.The pre-amplifier gain was set at 100 and the data points from the lock-inamplifier were read in millivolt. The thermal diffusivity error is mainly due tothe gradient and is about 4%.

Fig. 3: In(PE signal) versus cavity length for 6.4w % of sucrose in water

The FWHM was obtained by fitting the inphase signal by using the valueobtained from the experiment. This is because the magnitude and phase dataobtained were limited up to certain value of L immediately after the minimumvalley before the noise starts to dominates at large L. The fitting constant wasthen used to extrapolate the curve slightly beyond the small peak that is notactually covered by the experimental data points (Fig. 4). This is acceptablebecause it is merely extending the data points by fitting the existing experimentaldata so that the FWHM of the curve can be determined.

The plot of sucrose solution thermal diffusivity ci versus w% sucrose, Fig. 5,shows that a' decreases linearly with w% starting from the value for the plainwater or for Ow% sucrose. This corresponds very well with the simple mixturerule of Eqn. (6) for sucrose solution up to about 51.2w%. From the plot, thewater thermal diffusivity obtained from the intersection of the fitted line to theverticle axis is 0.144 x 1O-2 cm2/s, that is similar to the one obtained by Balderas­Lopez et al. (2000) by using the technique. From this linear relationship, thethermal diffusivity of the saturated solution (51.2w% sucrose) is 0.102 x 10-2

cm2/s. It is accepted that, for liquids, the thermal diffusivity decreases with

PertanikaJ. Sci. & Technol. Vol. 14 Nos. 1 & 2, 2006 37

Azmi, B.Z., Sing, L.T., Saion, E.B. & Wahab, ZA.

Fig. 4: In-phase signal versus cavity length at 6. 4w % of sucrose in water

•

•

'0 ~ J.oWn h1 porCOI1 go (%)

1 ~

1 >1 •

•13

1 2

j,

0 10

Fig. 5: Plot of thermal diffusivity versus sucrose w %

increasing molecular size. Here, the sucrose molecule is bigger in dimensioncompared to water, hence increasing the sucrose w% decreases the thermaldiffusivity of the solution. For the very high concentration value, i.e. higherthan 51.2w%, the thermal diffusivity would be constant and has the value ofthat of 51.2w% because the undilluted sucrose crystal settles at the bottom ofthe cavity instead of suspended homogenously in the solution.

The plot of mixture thermal diffusivity a' of sucrose solution versus (FWHM)2,Fig. 6, shows that a' increases linearly with (FWHM) 2. This indicates that therelationship of a' and FWHM can takes the following form;

38 PertanikaJ. Sci. & Techno!. Vo!. 14 Nos. 1 & 2,2006

Thermal Wave Resonant Cavity Technique in Measuring Thermal Diffusivity of Sucrose Solution

ci = M X (FWHM)2 + N,

where M is the gradient (8.099 ± 0.527 S-l) and N is the intersection with verticleaxis ci (0.092 x 1O-3 ± 0.075 X 10-3 cm.s-l

). A few scattered points are due to erorsin determining FWHM of a particular w% sucrose. This implies that FWHM canbe a sensitive indicator to liquid thermal diffusivitiy changes.

150

./

I 1

•100

~ ~ 1.m :n I.M

F'I/lJHM I,xHtcnti

Fig. 6: Liquid mixture thermal diffusivity versus (FWHM'f

CONCLUSION

Thermal diffusivity values for sucrose solution up to saturated solution can beexpressed using a simple mixture rule. The thermal diffusivity value of water isvery close to the literature value. The square of FWHM varies linearly withthermal diffusivity of sucrose solution up to sucrose saturated solution.

ACKNOWLEDGEMENT

The authors are grateful to the Ministry of Science, TechnologyEnvironment of Malaysia for supporting this work under IRPA Grant04-0132-EAOOl.

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Azmi, B.Z., Sing, L.T., Saion, E.B. & Wahab, ZA.

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